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This paper presents two theorems concerning the nonlinear differential equation x″+c(t)f(x)x′+a(t,x)=e(t), where e(t) is a continuous square-integrable function. The first theorem gives sufficient conditions when all the solutions of this equation are bounded while the second theorem discusses when all the solutions are in L2[0,∞)

international journal of mathematics and mathematical sciences

Bounded and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$L^2$" id="E1"><mml:mrow><mml:msup><mml:mi>L</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:math>-solutions to a second order nonlinear differential equation with a square integrable forcing term

Bounded andL2-solutions to a second order nonlinear differential equation with a square integrable forcing term